4. Write definitions for the following two functions: sumN (n) returns the sum of the first n natural numbers. sumNCubes (n) returns the sum of the cubes of the first n natural numbers. Then use these functions in a program that prompts a user for ann and prints out the sum of the first n natural numbers and the sum of the cubes of the first n natural numbers.
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- Complete the function that calculates the sum of the first n+1 terms of the geometric series a, ar, ar² ar³, ar4 . note that the series begins with a and the last term is ar", in total there are n+1 terms. ar" ... [ ]: # complete the function given the variables a,r,n and return the value as series_sum. def sum_geometric_series(a,r,n): # your code here return series_sumWrite a program that calculates the Euclidean distance and the Manhattan or taxicabdistance between two two-dimensional points. Make sure you 1) use a point structureto store the points (see above), 2) use functions to calculate the two distances and3) ask the user for the point data. The Euclidean distance is calculated using thePythagorean Theorem for (points (x1,y1),and (x2, y2):euclidean = ( x1-x2)^2 + ( y1-y2)^2And the Manhattan distance is calculated as:manhattan = | x1-x2 | + | y1-y2 |Write the following function to draw a regular polygon:def drawPolygon(x = 0, y = 0, radius = 50, numberOfSides = 3):The polygon is centered at (x, y) with a specified radius for the bounding circle for the polygon and the number of sides. Write a test program that displays a triangle, square, pentagon, hexagon, heptagon, and octagon, as shown in Figure 6.12a.
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